Finite element simulation of non-linear acoustic generation in a horn loudspeaker

The loudspeaker is an electro-acoustic device for sound reproduction which requires the distortion as small as possible. The distortion may arise from the magnetic non-linearity of the york, the uneven magnetic field distribution, the mechanical non-linearity at the diaphragm suspension and the acoustic non-linearity due to the high sound pressure and velocity in the duct-radiation system. A horn is sometimes provided in front of the vibrating diaphragm radiator, which plays an important role to increase the efficiency by matching the acoustic impedance between the radiator and the ambient medium. The horn is in many cases folded twice or three times to shorten the length, which further degrades the reproduction quality. The sound intensity and velocity are apt to attain very high in the small cross-sectional area in the throat and in the folded regions, which may cause the distortion due to the non-linear effect of the medium. The present paper is to investigate the frequency characteristics of the loudspeaker numerically evaluating the generation of the harmonics and sub-harmonics. An axisymmetric folded horn is considered for which the wave equation with the non-linear term retained is solved by the finite element method. The solution is made in time domain in which the sound pressure calculated at the opening end of the horn is Fourier-transformed to the frequency domain to evaluate the distortion, while the wave marching in the horn is visualized.     

CAN: an example of nonclassical acoustic nonlinearity in solids

A new class of nonlinear acoustic phenomena has been observed for acoustic wave interaction with simulated and realistic nonbonded contact interfaces (cracked defects) in solids. "Nonclassical" effects are due to substantially asymmetric stiffness characteristics of the interface for normal stress that results in specific contact acoustic nonlinearity (CAN). The asymmetry in the contact restoring forces causes the stiffness parametric modulation and instability of oscillations, which results in acoustic wave fractional subharmonic generation. The CAN subharmonics and higher harmonics reveal threshold dynamic behaviour, evident hysteresis, and instability effects.     

Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation

The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analyzed in the second part of this paper. A test rig is built corresponding to a double sphere-plane contact preloaded by the weight of a moving cylinder. Typical response curves are obtained for several input levels. Time traces and spectral contents are explored. Both amplitude and phase of harmonics of the dynamic response are investigated.Linearized resonance frequency and damping ratio are identified from the almost linear behaviour under very small input amplitude. Increasing the external input amplitude, the softening behaviour induced by Hertzian non-linear stiffness is clearly demonstrated. The resonance peak is confined to a narrow frequency range. Jump discontinuities are identified for both amplitude and phase responses. The forced response spectrum exhibits several harmonics because of a non-linear Hertzian restoring force. Numerical simulations show a very good agreement with experimental results.For higher input amplitudes, the system exhibits vibro-impacts. Loss of contact non-linearity clearly dominates the dynamic behaviour of the vibro-impacting contact and leads to a wide frequency range softening resonance. The spectral content of the response is dominated by both the first and the second harmonics. Evolution of the experimental downward jump frequency vs. input amplitude allows the identification of the non-linear damping law during intermittent contact. Simulations of the vibro-impacting Hertzian contact are performed using a shooting method and show a very good agreement with experimental results.     

The detectability of kissing bonds in adhesive joints using ultrasonic techniques

This paper concerns a study of the detectability of dry contact kissing bonds in adhesive joints using three ultrasonic inspection techniques. Conventional normal incidence longitudinal and shear wave inspection were conducted on dry contact kissing bonds using a standard damped ultrasonic transducer and an electro-magnetic acoustic transducer (EMAT) respectively. The detectability of the dry contact kissing bonds was assessed by calculating the reflection coefficient of the imperfect interface at varying loads for a number of surface roughnesses. A high power ultrasonic method was also employed to determine the non-linear behavior of the adhesive interface. The non-linearity of the interface was determined by the ratio of the amplitudes of the first harmonic and fundamental frequencies of the transmitted waveform. It was found that the high power technique showed the greatest sensitivity to these kissing bonds at low contact pressures, however at high loads conventional longitudinal wave testing was more sensitive. It was also noted that a combination of two or more techniques could provide enhanced information about the kissing bond compared to a single technique alone.     

Characterization of biological media by means of their non-linearity

This review presents the state-of-the-art in applications of the second order acoustic non-linearity parameter, B/A, for the characterization of biological media. The close relationship between B/A and the molecular structure of certain liquids, as well as the influence of the inhomogeneous nature of biological materials on B/A, are discussed. The finite amplitude and the thermodynamic methods are presented, and their advantages, disadvantages and accuracy of data produced are discussed. A new and promising procedure, real time non-linear parameter tomography, is critically evaluated and its prospective application for in vivo studies is treated in some depth. B/A values covering a broad variety of biological materials are presented and a world-wide collaborative research scheme is suggested for systematic and in-depth studies of non-linearity of biological media and for clinical exploitations of the results of these studies.     

Non-linear vibrations of cables in three dimensions,part I: Non-linear free vibrations

Analysis and results for non-linear free vibrations of both horizontal and inclined cables in three dimensions are presented. Sag-to-span ratios of the cables are not limited to being small. Computed results are presented for various geometrical and material parameters. The major findings are that the geometrical non-linearity may be of the stiffening type or the softening type, depending on the sag-to-span ratio, and the stiffness of out-of-plane vibrations is affected by the corresponding in-plane vibration near a resonant frequency due to non-linear coupling between out-of-plane and in-plane vibrations.     

Harmonic generation of an obliquely incident ultrasonic wave in solid-solid contact interfaces

The conventional acoustic nonlinear technique to evaluate the contact acoustic nonlinearity (CAN) at solid-solid contact interfaces (e.g., closed cracks), which uses the through-transmission of normally incident bulk waves, is limited in that access to both the inner and outer surfaces of structures for attaching pulsing and receiving transducers is difficult. The angle beam incidence and reflection technique, where both the pulsing and receiving transducers are located on the same side of the target, may allow the above problem to be overcome. However, in the angle incidence technique, mode-conversion at the contact interfaces as well as the normal and tangential interface stiffness should be taken into account. Based on the linear and nonlinear contact stiffness, we propose a theoretical model for the reflection of an ultrasonic wave angularly incident on contact interfaces. In addition, the magnitude of the CAN-induced second harmonic wave in the reflected ultrasonic wave is predicted. Experimental results obtained for the contact interfaces of A16061-T6 alloy specimens at various loading pressures showed good agreement with theoretical predictions. Such agreement proves the validity of the suggested oblique incidence model.     

Pulse propagation in a nonlinear dielectric slab waveguide

The evolution of an optical pulse in a single-mode, step index dielectric slab waveguide which is characterized by an intensity dependent dielectric function in the core and cladding regions is treated by means of differential equation techniques. A cubic order non-linearity is considered. The electromagnetic field distribution in the slab waveguide region satisfies a non-linear wave equation. This field can be represented in terms of even TE guided modes with a slowly varying envelope amplitude function.Then using the well known approximation, based on the slowly varying character of the amplitude function, a non linear partial differential equation is obtained for the amplitude function. As the coefficients of this equation depend on the distance across the transverse direction X, an averaging technique over x is applied to reduce the nonlinear partial differential equation into a form that is easily transformed to the so-called non-linear Scroedinger differential equation.This equation is then attacked by means of the well known Inverse Scattering method in the case of reflection less potentials. The single and double soliton solutions are obtained explicitly for a single-mode slab waveguide. Finally numerical results are presented in the time domain.     

Non-linearity parameter B/A of binary liquid mixtures at elevated pressures

When sound waves of high amplitude propagate, several non-linear effects occur. Ultrasonic studies in liquid mixtures provide valuable information about structure and interaction in such systems. The present investigation comprises of theoretical evaluation of the acoustic non-linearity parameter B/A of four binary liquid mixtures using Tong and Dong equation at high pressures and T=303.15 K. Thermodynamic method has also been used to calculate the non-linearity parameter after making certain approximations.     

激励Brillouin散射非线性致稳过程的阻尼效应

本文研究了由非线性引起的Brillouin散射致稳效应。我们主要兴趣是Landau阻尼对非线性致稳的影响。我们求解了时间、空间和时-空有关的方程,得到了场能密度、场幅、饱和时间和空间大小等随物理参量变化的近似解析表达式。 关键词：     

Solitary wave emission from a non-linear waveguide with a PTS cladding

We present numerical simulations of solitary wave emission from a waveguide in which the cladding is the non-linear material polydiacetylene para-toluene sulfphonate (PTS). In addition to a self-focusing cubic non-linearity PTS exhibits a defocusing quintic non- linearity, which imposes a limit on the peak non-linear index change. The influence of this limiting on solitary wave emission is studied in detail in one transverse dimension, and we show that it can increase the fraction of the incident power transferred into the emitted solitary wave. Fabrication issues arising from the limiting are also discussed. Numerical simulations in two transverse dimensions are also presented showing stable emitted solitary waves due to the stabilizing effect of the limiting, in contrast to the self-focusing collapse which occurs for a cubic non-linearity.     

Propagation of initially bi-harmonic sound waves in a 1D semi-infinite medium with hysteretic non-linearity

Materials with hysteretic non-linearity have the property of memorizing specific previous extrema in the stress/strain loading history. Because of this complexity, the analytical theory describing the non-linear evolution of acoustic waves in such materials is currently restricted to simplex wave propagation processes with a single minimum and a single maximum over a wave period. In the present paper a numerical model is presented which is valid for an arbitrary strain wave profile, and the results for the frequency-mixing process in acoustic waves composed initially of two harmonic frequency components are analyzed. The model simulations demonstrate that an initially complex wave transforms into a simplex wave during propagation. In addition, we have studied the mutual influence of the initial frequency components, and we have found regimes of induced absorption and induced transparency.     

Breathing pulses and beams innon-linear media

Oscillating solutions are known to exist for the (1+1)-dimensional non-linear Schrödinger equations (NLSE) with Kerr non-linearity and for (3+1)-dimensional and (2+1)-dimensional NLSE with saturable non-linearity. In them, there is an interplay between the amplitude and the widths of the solutions. Using the variational method, we show that non-linear Schrödinger equations with Kerr non-linearity support breather-like solutions in the form of oscillating spatiotemporal pulses and beams but unlike the cases mentioned above, the oscillating behaviour takes place between the widths, with the amplitude kept almost constant. For the space–time NLSE these solutions exist only in a medium with anomalous dispersion.     

Non-linear free torsional vibrations of thin-walled beams with bisymmetric cross-section

A finite element method for studying non-linear free torsional vibrations of thin-walled beams with bisymmetric open cross-section is presented. The non-linearity of the problem arises from axial loads generated at moderately large amplitude torsional vibrations due to immovability of end supports. The derivation of the fundamental differential equation of the problem is based on the classical assumption of a thin-walled beam with a non-deformable cross-section. The non-linear eigenvalue problem is solved iteratively by series of linear eigenvalue problems until the required accuracy is obtained. Non-linear frequencies, fundamental mode shapes and axial loads computed for various amplitude of torsional vibrations of thin-walled I beams are included.     

Experimental and theoretical study of harmonic generation at contacting interface

The second harmonic generation behavior of a contacting interface has been evaluated experimentally and discussed theoretically in the light of a nonlinear interface model. Two aluminum blocks were mated together to constitute a contact interface and subjected to normal compressive loading. A 5 MHz longitudinal toneburst wave was sent to the interface in the normal direction and the transmitted wave was recorded, from which the fundamental and the second harmonic components were extracted. A nonlinearity parameter was obtained as the ratio of the second harmonic amplitude to the squared fundamental amplitude. From the measured contact pressure dependence of the transmitted fundamental amplitude, the linear and the second-order interfacial stiffness parameters were identified, which enabled the evaluation of the nonlinearity parameter based on the theoretical model. The theoretical contact pressure dependence of the nonlinearity parameter was found to be in good qualitative agreement with the experimental results.     

Finite-amplitude longitudinal waves in non-uniform bars

An analysis is presented of the non-linear propagation of longitudinal waves along a bar whose geometrical and material properties vary slowly along its length, taking into account the effects of a small viscosity. A first-order uniform expansion for small but finite amplitudes is obtained by using the method of multiple scales. The analytical solution shows the effects of non-linearity, heterogeneity, and dissipation on the distortion of the waves and the formation of shock waves. The present results show that if the speed of sound or the cross-sectional area of the rod decreases in the direction of propagation, the wave amplitude and the rate of progress of finite-amplitude distortion increase as the wave propagates.     

Sound wave propagation in weakly polydisperse granular materials

Dynamic simulations of wave propagation are performed in dense granular media with a narrow polydisperse size-distribution and a linear contact-force law. A small perturbation is created on one side of a static packing and its propagation, for both P- and S-waves, is examined. A size variation comparable to the typical contact deformation already changes sound propagation considerably. The transmission spectrum becomes discontinuous, i.e., a lower frequency band is transmitted well, while higher frequencies are not, possibly due to attenuation and scattering. This behaviour is qualitatively reproduced for (i) Hertz non-linear contacts, for (ii) frictional contacts, (iii) for a range of smaller amplitudes, or (iv) for larger systems. This proves that the observed wave propagation and dispersion behaviour is intrinsic and not just an artifact of (i) a linear model, (ii) a frictionless packing, (iii) a large amplitude non-linear wave, or (iv) a finite size effect.     

Dust acoustic shock wave generation due to dust charge variation in a dusty plasma

In a dusty plasma, the non-adiabaticity of the charge variation on a dust grain surface results in an anomalous dissipation. Analytical investigation shows that this results in a small but finite amplitude dust acoustic (DA) wave propagation which is described by the Korteweg-de Vries-Burger equation. Results of the numerical investigation of the propagation of large-amplitude dust acoustic stationary shock wave are presented here using the complete set of non-linear dust fluid equations coupled with the dust charging equation and Poisson equation. The DA waves are of compressional type showing considerable increase of dust density, which is of significant importance in astrophysical context as it leads to enhanced gravitational attraction considered as a viable process for star formation. The DA shock transition to its far downstream amplitude is oscillatory in nature due to dust charge fluctuations, the oscillation amplitude and shock width depending on the ratioω _pd/V_ch and other plasma parameters Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

水下声辐射激励水表面声波的特征参数测量

采用激光干涉方法对水下声辐射激励水表面声波的特征参数频率和振幅进行了测量研究。从理论上对水表面声波激光相干测量信号的频谱构成进行了分析,在此基础上提出了水表面声波两个重要声学参数频率和振幅的解算方法,并通过数值仿真进行了验证。搭建了一套简单的激光干涉测量实验系统,对不同频率和声压激励的水表面声波进行了测量实验,验证了水表面声波频率和振幅解调方法的准确性。对水表面声波横向传播的振幅衰减现象进行了初步的实验研究,结果表明水表面声波的频率越高,振幅的横向衰减越快。研究表明激光相干检测方法能够准确地实现水表面声波振幅和频率的测量。      

Self-consistent renormalized phonons in metallic and nonmetallic solids

The interaction of charged particle beam with non-linear “cubic” type media has been studied; the dielectric permeability of such media depends on the square strength of the electric field produced by the beam-excited wave. The processes of the Cherenkov excitation of the medium by a modulated definite current are investigated as well as the polarization of longitudinal oscillations of the medium excited by the current. The equations are obtained to determine the dependence of fields excited by the current on the amplitude of the exciting current. It is found that under certain circumstances (near the radiation cut-off) the conditions of Cherenkov radiation may be violated due to non-linearities of the medium and the particle radiation loss vanish. The amplification of longitudinal waves in an arbitrary isotropic medium with “cubic” non-linearity by a monoenergetic particle beam is studied when the frequencies of amplified oscillations are close to the resonance frequencies of the medium.